## Dipartimento di Fisica Università di Roma "La Sapienza "

Queste del suo cervel mere invenzioni le vende per misteri, e son canzoni.## (G. Busenello dall'Incoronazione di Poppea di Monteverdi)

**RELATORE:**M. Zaiser (Max Plank Institut, Stuttgart, Germany.)**TITOLO:**"Fractal dislocation patterning in plastic deformation"**ABSTRACT:**Plastic deformation of crystalline solids is due to the motion of line defects (dislocations). In a continuum framework, dislocations can be invisaged as line singularities in an elastic continuum. They interact via long-range elastic fields decreasing as 1/r with distance r from the dislocation lines. In the course of deformation, moving dislocations entangle to form three-dimensional spatially inhomogeneous networks. Observations of two dimensional sections using transmission electron microscopy indicate that these networks can, over a range of scales typically between 0.1 and 10 micrometers, be envisaged as random fractal sets with dimensions between 2 and 3. Examples of fractal dislocation patterning are presented, and methods to determine dimensions of such patterns are discussed. Some long-standing problems of quantitative metallography are revisited from a fractal geometry viewpoint. In conclusion, some potential mechanisms for the formation of fractal dislocation arrangements, and dislocation patterning in general, are outlined.

**RELATORE:**Silvio Franz (ICTP, Trieste, Italy)**TITOLO:**"Principio di Regressione alla Onsager nella Dinamica Vetrosa"**ABSTRACT:**

**RELATORE:**Prof. Alan D.Sokal (Dep.of Physics, New York University)**TITOLO:**"Monte Carlo algorithms for self-avoiding walk"**ABSTRACT:**This talk is a review of Monte Carlo algorithms for generating self-avoiding walks. I begin by examining static Monte carlo algorithms: simple sampling and its variants, and dimerization. The bulk of the talk is devoted to dynamic (Markov-chain-based) Monte Carlo algorithms, which I shall classify as local, bilocal or non-local. For each algorithm, I discuss two key problems: the algorithm's ergodicity, and its dynamic critical behavior.

**RELATORE:**Prof. J. Swart (South Africa)**TITOLO:**"The effects of habitat fragmentation on Samango monkeys survival".**ABSTRACT:**Many monkey populations face forest fragmentation and persist as metatpopulations. A stochastic, spatial population model is developed, which takes into account the effects of demographic and environmental stochasticity, and natural catastrophes. We compare the management options of reintroduction of troops and of providing corridor links between patches in a metapopulation.

**RELATORE:**Prof. Constantino Tsallis (CBPF, Rio de Janeiro)**TITOLO:**: Nonextensive statistical mechanics and thermodynamics: recent results.**ABSTRACT:**It is since long known that standard statistical mechanics and thermodynamics have restrictions when the system presents long-range interactions, long-range microscopic memory and others. We have recently proposed a generalization of the standard formalism in order to cover such nonextensive situations. Applications are now available for Levy-type and correlated-type anomalous diffusions, turbulence in pure-electron plasma in the presence of external magnetic field, solar neutrino problem, nonlinear dynamical systems and others. The formalism will be introduced and the present status reviewed.

**RELATORE:**Dr. J. Kurchan (Ecole Normale Paris)**TITOLO:**Dinamica vetrosa in sistemi non puramente dissipativi**ABSTRACT:**

**RELATORE:**Dr. Marco Picco (LPTHE, Univ. Paris 6 & Paris 7)**TITOLO:**:Numerical results for 2D Potts models with weak randomness.**ABSTRACT:**Recent numerical results for 2D Potts models with weak disorder are presented. A comparison is made with previous results as well as with analytical ones.

**RELATORE:**Prof. Khrennikov (Mosca)**TITOLO:**:p-adic stochastic, dynamical system and quantization.**ABSTRACT:**

**RELATORE:**Dr. Filippo Cesi(Universita La Sapienza)**TITOLO:**: Dinamica di sistemi di spin random nel regime di Griffith**ABSTRACT:**Dopo un'introduzione alle problematiche generali della dinamica dei sistemi di spin, verranno discussi risultati recenti che riguardano interazioni random (es. spin-glass) nel regime di Griffiths.

**RELATORE:**Dr. Ugo Bastolla (Universita La Sapienza)**TITOLO:**: Dai sistemi dinamici disordinati ai processi stocastici: l'approssimazione annealed.**ABSTRACT:**Verra` presentato un nuovo metodo per calcolare le proprieta` statistiche di sistemi dinamici disordinati, basato sull'introduzione di opportuni processi stocastici. Questo metodo trova applicazione nello studio di modelli ispirati dalla biologia teorica, quali le reti booleane stocastiche proposte da Kauffman come modello dei sistemi di regolazione dell'attivita` dei geni, e le reti neuronali con asimmetrie sinaptiche.

**RELATORE:**Dr. William Bialek, NEC Research Laboratories, Princeton**TITOLO:**Neural coding of natural signals: methods from information theory**ABSTRACT:**Sensory signals are represented in the brain by trains of action potentials or spikes. Traditional studies of this representation use isolated, discrete signals, quite unlike the continuously varying signals that occur in the natural environement. I will discuss the use of information theory to design and analyze new experiments on the representation of more natural signals in single neurons. The results illustrate the importance of action potential timing and the adaptation of the neural code to the natural environment

**RELATORE:**Daniel A. Stariolo (INFN sez Roma "La Sapienza")**TITOLO:**Generalized Simulated Annealing**ABSTRACT:**We propose and illustrate a new stochastic algorithm ( generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm recovers, as particular cases, the so called classical (``Boltzmann machine'') and fast (``Cauchy machine'') simulated annealings, and turns out to be quicker than both.

**RELATORE:**Prof. Robert Suris (Ioffe, Mosca)**TITOLO:**Modelling of Crystal Growth and Selforganizing Processes in Molecular Beam Epitaxy**ABSTRACT:**An analytical consideration of the 2D nuclei evolution during the epitaxial growth will be given. The results for the time evolution of the nuclei size distribution function will be presented. The results on the surface stability and on the possibility of selforganizing processes during the epitaxial growth will be presented. These results will be discussed together with results of our Monte-Carlo simulation of growth processes.

**RELATORE:**Dr. J.J. Ruiz-Lorenzo (INFN sez Roma "La Sapienza")**TITOLO:**Recenti risultati numerici in vetri di spin tridimensionali.**ABSTRACT:**Verranno presentati alcuni risultati numerici, statici e dinamici, ottenuti simulando un vetro di spin tridimensionale su calcolatore APE-100. Verrano presentate inoltre evidenze numeriche di come la fase di bassa temperatura sia di tipo Mean Field.

**RELATORE:**Prof. Vladimir Dotsenko (Paris VI)**TITOLO:**Conformal Field Theory Approach to 2D Critical Systems with Randomness.**ABSTRACT:**Several 2D statistical models with randomness are studied at their critical points by using the renormalization group (RG) approach based on conformal field theory. For the particular case of randomly coupled minimal models we suggest an exact result for the corresponding RG flow. Other results are of an \epsilon expansion perturbative nature. Some results of numerical simulations are to be given.

**RELATORE:**Prof. Peter Young (UCSC, CA)**TITOLO:**"Critical Behavior and Griffiths-McCoy Singularities in Quantum Spin Glasses"**ABSTRACT:**

**RELATORE:**Prof. I. Kondor (Budapest)**TITOLO:**Peculiar features of continous replica simmetry breaking**ABSTRACT:**

**RELATORE:**Prof. Heinz Horner (Heidelberg)**TITOLO:**Off-equilibrium dynamics of disordered mean-field systems**ABSTRACT:**Glasses, Spin glasses and other disordered systems show relaxation processes and aging phenomena on extremely long time scales. In certain limits (infinite range of interaction, infinite dimension) corresponding models are solved exactly by mean field theory. For spherical models the resulting dynamic mean field equations can be writen down in a closed form. As a first example I discuss the steady state motion of a particle in a random potential under the influence of a driving force. Depending on temperature and range of the correlations of the random potential, phases with normal drift, creep or pinning are found. The phase diagram differs from the one derived from static replica theory. The dynamics is ruled by the intrinsic time scale, the external time scale (inverse drift velocity) and two additional intermediate time scales. As a second example I discuss the relaxation of a spherical p-spin glass from a fully magnetized initial state. Depending on temperature and applied field, again various phases can be distinguished. In one of the phases anomalous aging is found.

**RELATORE:**Dr. Marco Ferrero (Roma, "La Sapienza")**TITOLO:**Rottura spontanea della simmetria delle repliche e divergenze infrarosse nel modello di Ising Spin Glass.**ABSTRACT:**Verranno presentati e discussi i problemi connessi alle divergenze infrarosse che appaiono nella analisi delle fluttuazioni del parametro d'ordine intorno alla soluzione di Parisi per il modello di Ising Spin Glass in approssimazione di campo medio.

**RELATORE:**Dr. Paola Ranieri (Roma, "La Sapienza")**TITOLO:**Dinamica Critica dei Vetri di Spin: Fluttuazioni non locali in un modello Short-Range.**ABSTRACT:**Viene considerata una versione soft-spin del modello di Edwards-Anderson che evolve secondo l'equazione di Langevin. Si determina l'andamento dei propagatori dinamici non locali per $T\rightarrow T_{c}^{+}$, e si costruisce la teoria delle perturbazioni. Risultati preliminari ad un loop sembrano confermare la relazione di scaling per l'esponente dinamico $z=2(2-\eta)$. Ulteriori verifiche sono comunque necessarie.

**RELATORE:**Dr. Denis Bernard (CEA-Saclay, Paris)**TITOLO:**Anomalous scaling of a passive scalar in a turbulent flow.**ABSTRACT:**The passive scalar problem consists in describing the statistical behavior of a scalar field, e.g. the temperature, in a turbulent flow. We will describe how recent studies of a simple version of this problem formulated by Kraichnan lead to some understanding of the origin of the breakdown of the Kolmogorov inertial-range scaling of the scalar correlation functions.

**RELATORE:**Dr. David Lancaster(INFN Roma "La Sapienza")**TITOLO:**A Field theory for site disordered spins.**ABSTRACT:**A replica theory describing diluite spin systems is developed. It is based on the notion of grand canonical disorder and is analysed using a variational method.

**RELATORE:**Dr. Alan Drory (Roma "La Sapienza")**TITOLO:**Some Theoretical Calculations in Continuum Percolation**ABSTRACT:**In the last two decades there have been several calculations of the percolation threshold in continuum (off-lattice) systems. These allow us, in principle, to consider the influence of dimensionality, inter-particle interaction and object shape on the connectivity properties of a system.

**RELATORE:**Prof. Ian Drummond (Cambridge)**TITOLO:**Diffusion in random gradient flow.**ABSTRACT:**The effective diffusivity in a random background irrotational velocity field is calculated by a renormalization group method with surprisingly accurate results.

**RELATORE:**Dr. Erik Aurell (Math Dept., Stockholm University, Sweden)**TITOLO:**Option Pricing and Partial Hedging: Theory of Polish Option.**ABSTRACT:**Using a recent theory of Bouchaud and Sornette we develop a theory of option pricing on the Warsaw Stock Exchange. We compute bid and ask prices for buyers and sellers of such hypothetical options, and identify a price where they meet. This price reduce to the Black and Scholl price in the appropriate limit. This is joint work with K. Zycrkowsky.

**RELATORE:**Prof. T.M._Nieuwenhuizen (University of Amsterdam)**TITOLO:**Exactly solvable quantum spin glasses; Complexity as the driving force for dynamical glassy transitions.**ABSTRACT:**The mean field spherical model with both random pair and random quartet interactions has a Ginzburg-Landau expansion similar to the one of the Sherrington-Kirkpatrick model. Due to the Gaussian nature of spherical spins, the model can be solved exactly at any temperature. The unphysical behavior at low temperatures is healed by quantizing the spherical model in general.

In mean field spin glass models with one step of replica symmetry breaking there occurs a dynamical phase transition at a temperature higher than the static transition. Its replica free energy lies below the paramagnetic one, and has a larger slope. It is explained that this is due to the complexity, which thus drives the phase transition. A related fact is that the specific heat differs from the internal energy fluctuations, with the `wrong' inequality.

**RELATORE:**Prof. M.H. Jensen(Niels Bohr Institute, Copenhagen)**TITOLO:**Depinning and Multiscaling for Dynamical Interfaces.**ABSTRACT:**The dynamics of self-affine interfaces is often described in terms of the KPZ equation. If the interface penetrates a quenched random medium this description fails and quenched random noise must be added, as first discussed by Parisi. Sneppen introduced a simple model that describes the motion around the depinning point. It is found that the motion occurs in localized avalanches giving rise to dynamical multiscaling. The model can be understood by mapping it onto directed percolation and we discuss recent advances in this theory, as proposed by various groups.

**RELATORE:**Prof. Koji Nemoto (Hokkaido University, Sapporo, Japan)**TITOLO:**Exchange Monte Carlo Method and Application to Spin Glass Simulations**ABSTRACT:**We propose an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional +/- J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.

**RELATORE:**Dr. David Dean (INFN Roma "La Sapienza")**TITOLO:**"Aging on trees. A model for spin glass dynamics."**ABSTRACT:**We discuss a semi-phonomenological model which can be used to implement the ideas of replica symmetry breaking for spin glass statics into spin glass dynamics. The model can be exactly solved in the long time regime and the results compared with experiments on TRM decay.

**RELATORE:**Dr. Felix Ritort (Univ. Carlos III, Madrid)**TITOLO:**"Analytical solution of the Monte Carlo dynamics of a simple spin-glass model"**ABSTRACT:**We present an exact solution of the Monte Carlo dynamics of the spherical Sherrington-Kirkpatrick spin glass model. We obtain the dynamical equations for a generalized set of moments which can be exactly closed. In a certain particular limit the dynamical evolution of the system coincides with the Langevin dynamics.

**RELATORE:**Prof. Marc Mezard (Ecole Normale, Paris)**TITOLO:**"Scaling and intermittency in Burgers turbulence".**ABSTRACT:**We study the fully developped turbulence in the $N$ dimensional forced Burgers' equation, using the mapping between Burgers' equation and the problem of a directed polymer in a random medium. This allows to compute the full probability distribution function for velocity differences $v(x)-v(y)$ in the inertial regime. We find strong intermittency effects, directly related to the existence of large scale structures which are the generalizations of the usual shocks in the one dimensional Burgers problem. Technically this intermittency is related to the replica symmetry breaking in the directed polymer problem.

Giulia Iori(iori@chimera.roma1.infn.it) Roberto D'Autilia